A Reproducible Weak-Grid Benchmark with Switching-Averaged EMT Validation for Battery-Backed Grid-Forming Control in PV Microgrids

Controller comparisons for grid-forming battery inverters are often confounded by simultaneous changes in the plant model, saturation law, measurement filtering, and disturbance envelope. This paper addresses that problem through a reproducible weak-grid benchmark and a switching-averaged EMT validation layer for a battery-backed PV microgrid. Droop, virtual synchronous machine (VSM), and power-synchronization control (PSC) are compared under identical plant data, load disturbance, grid-strength reduction, voltage sag, current limit, and metric-extraction rules. The benchmark reveals a consistent trade-off: VSM provides the best frequency moderation, droop provides the fastest post-fault restoration and the lowest implementation burden, and PSC provides the most balanced compromise across recovery, stability, EMT, and implementation metrics. The averaged EMT layer preserves the low-order restoration ordering and sharpens the waveform trade-off during the fault window. Additional analyses quantify the converter-angle excursions during the sag, clarify the reduced lag tolerance of VSM as the grid becomes weaker, and test the local robustness of the reported ranking against representative tuning perturbations. The resulting message is benchmark-specific but operationally useful: controller selection should follow the dominant project objective—frequency quality, restorative efficiency, or balanced performance—before controller-specific switching EMT, hardware-in-the-loop, and plant-level studies are launched.